In an experiment conducted using the Young's double-slit apparatus, the separation between the slits is 20 µm. A first-order constructive interference fringe appears at an angle of 2.5o from the zeroth order (central) fringe.

A. What wavelength of light is used in the experiment?

B. At what angle would the fourth-order (m = 4) bright fringe appear?

C. At what angle would the fourth-order (m=4) dark fringe appear?

Question

Grace Hill

Physics

26 August, 16:18

In an experiment conducted using the Young's double-slit apparatus, the separation between the slits is 20 µm. A first-order constructive interference fringe appears at an angle of 2.5o from the zeroth order (central) fringe.

A. What wavelength of light is used in the experiment?

B. At what angle would the fourth-order (m = 4) bright fringe appear?

C. At what angle would the fourth-order (m=4) dark fringe appear?

+1

Answers (1)

Know the Answer?

Yahir Holmes · Answer 1

To solve this problem, we use the formula

λ = s sin θ

where s is the separation and θ is the angle interference

So,

λ = 20 x 10^-6 sin 2.5

λ = 8.72 x 10^-7 m

The required angle for the fourth order bright fringe is

θb = sin⁻¹ (4λ / s) = sin⁻¹ (4 (8.72 x 10^-7 m) / 20 x 10^-6) = 10.04°

The required angle for the fourth order dark fringe is

θd = sin⁻¹ (4.5 λ / s) = sin⁻¹ (4.5 (8.72 x 10^-7 m) / 20 x 10^-6) = 11.31°